Base 3 addition

Number Theory Level 2

What is the sum of 2222 2 3 + 2222 2 3 22222_3 + 22222_3 in base 3 3 ?

Write your answer in base 10 10 .


The answer is 484.

Ossama Ismail by Ossama Ismail , 63, Egypt

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1 solution

Marta Reece
Jan 1, 2018

( 81 + 27 + 9 + 3 + 1 ) × ( 2 + 2 ) = 484 (81+27+9+3+1)\times(2+2)=\boxed{484}

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Maximum number that can be written in any base system in n n locations = base n − 1 \text{base}^n -1

in this problem n = 5 n = 5 and b = 3 b =3 .

The value of 2222 2 3 = 3 5 − 1 = 242 22222_3 = 3^5 -1 = 242 then 2222 2 3 + 2222 2 3 = 2 ∗ 242 = 484 22222_3 + 22222_3 = 2*242 = 484

Ossama Ismail - 3 years, 5 months ago

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